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Numericals 1. Discuss the following functions to be taken as acceptable wave functions: Ne-ax2 iv: i: Neax ii: Neax ii: Ne-ax² 5-x A wave function is given by w(x) = Nekx in the region 0

Numericals 1. Discuss the following functions to be taken as acceptable wave functions: Ne-ax2 iv: i: Neax ii: Neax ii: Ne-ax² 5-x A wave function is given by w(x) = Nekx in the region 0

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Numericals 1. Discuss the following functions to be taken as acceptable wave functions: Ne-ax2 iv: i: Neax ii: Neax ii: Ne-ax² 5-x A wave function is given by w(x) = Nekx in the region 0 <x <a . Find the normalization %3D constant N. 3, Electrons with energies of 0.400 eV are incident on a barrier 3.0 eV high and 0.100 nm wide. Find the probability for these electrons to penetrate the barrier. (Ans T =19.20%) 4. A beam of identical electrons is incident on a barrier 6.0 eV high and 2 nm wide. Find the energy of the electrons if 1% of the electrons are to get through the barrier.(Ans =5.963eV) 5. An electron and a proton with the same energy E approach a potential barrier whose height U is greater than E. Comment on their tunneling probability. 6. A current beam 10 pico amperes (of identical electrons) is incident on a barrier 5.0 eV high and 1 nm wide. Find the transmitted current strength if the energy of the electrons is 4.9ev.(Ans = T=3.93% Transmitted current = 10pA *.0393 = 0.393PA) %3D %3D
Transcribed Image Text:Numericals 1. Discuss the following functions to be taken as acceptable wave functions: Ne-ax2 iv: i: Neax ii: Neax ii: Ne-ax² 5-x A wave function is given by w(x) = Nekx in the region 0 <x <a . Find the normalization %3D constant N. 3, Electrons with energies of 0.400 eV are incident on a barrier 3.0 eV high and 0.100 nm wide. Find the probability for these electrons to penetrate the barrier. (Ans T =19.20%) 4. A beam of identical electrons is incident on a barrier 6.0 eV high and 2 nm wide. Find the energy of the electrons if 1% of the electrons are to get through the barrier.(Ans =5.963eV) 5. An electron and a proton with the same energy E approach a potential barrier whose height U is greater than E. Comment on their tunneling probability. 6. A current beam 10 pico amperes (of identical electrons) is incident on a barrier 5.0 eV high and 1 nm wide. Find the transmitted current strength if the energy of the electrons is 4.9ev.(Ans = T=3.93% Transmitted current = 10pA *.0393 = 0.393PA) %3D %3D
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